The winger earned strong reviews during his debut top-flight season in 2018-19 despite Cardiff coming up short in their bid to avoid relegation to the Championship.
Such performances have seen him linked with Crystal Palace and Burnley, as well as Chelsea; speculation that could prove distracting for a 24-year-old looking to get back to the top of English football.
But Murphy insists that his attention is fixed firmly on the fortunes of Cardiff and helping Neil Warnock's side make an immediate return to the Premier League over the coming months.
"I can tell you I took no notice of it [being linked with Chelsea]. I don’t know if there’s any truth in it, but I took no notice of it," Murphy told Goal in an exclusive interview.
Josh Murphy: The footballing twin aiming to emulate Neymar
'We're both wingers, but we're two different types of wingers' Nizaar Kinsella spoke to Cardiff City Football Club forward Josh Murphy about twin brother Jacob, his footballing idols and wanting to be one of the best 🙌Posted by Goal.com on Friday, 5 July 2019
"I wouldn’t say it is a distraction, stuff like that is always going to happen. There is a fine line about it being true and not true.
"It is just something that I would never look into too deeply. It is the end of the season so you always get stuff like that. I see myself staying at Cardiff. Then we go from there.
"You never know what the future holds but as of now I am a Cardiff player and I am gearing up to get ready to fight for promotion to the Premier League.
"I have only been here for a season and I love it here. That’s my priority - to be at Cardiff and get Cardiff back to the Premier League."
While playing in the Championship can take a player away from the spotlight, the ever-increasing quality in England's second tier has started to be recognised by those at the very top of the game.
Daniel James has already completed a move to Manchester United following a breakout year for Swansea City in the Championship last term while Mason Mount's performances on loan at Derby County from Chelsea earned him a call-up to the England squad in October.
And Murphy, who has won youth caps at various England age-group levels, believes he too has what it takes to catch the eye of Three Lions boss Gareth Southgate ahead of the European Championship in 2020.
"I have always had that self-belief in myself. I have always thought I had enough talent and belief to make it to the very top. The only person who was going to stop me was me. Now I am eventually where I wanted to be, playing Premier League football.
"I feel like I did alright [in the Premier League]. I am always out there to improve and get better as a player. So, hopefully, I have impressed the right sort of people. I want to go out there and enjoy football, get goals and assists for the team and bring success to the club.
"Any young English player's dream is to play for England. Going through the England ranks, then my goal is to eventually play for the England team. That will come down to me, how well I play and if I can impress the right people. It is one of my dream goals to do and hopefully I can get there."
Murphy forms one half of English football's most famous active twins, with brother Jacob currently plying his trade for Newcastle.
Over the past few seasons the pair have been moved apart due to their respective transfers having played together for both QPR and Norwich City, having begun their footballing development at local London side Pitshanger Dynamo.
And Murphy believes that it has been hugely beneficial to have Jacob by his side throughout the early years of his career, saying: "Being twins, you are always going to have your brotherly rivalry. Some days you are going to hate him, some days you are going to love him.
"That’s like every brother and sister everywhere. We are always there to drive and push each other on.
"If he scored more goals than me as we got older, it is not like I am going to resent him. It would be his job to go to me and say ‘come on, I am going to help you be better'. We were always going to try to keep driving each along to keep getting better, better and better. I feel like we have done that.
"I used to be a centre-back and then Jacob played in midfield. As we started getting older, the positions started changing but they are my first early memories from playing football. I would stay at the back, smash it up for Jacob to run on and score.
"A lot of the scores would end up maybe 15-2 or 20-4 or something like that. That’s just the way it works. As you start developing and getting older, you start trying new things, like you want to play in different positions. Now both of us are wingers and we are enjoying ourselves.
"We would always get mistaken. Being identical twins, it is easy for that to happen. We are both wingers, but different types of wingers. I like to be out on the touchline, chalk on my boots and take defenders on one-versus-one.
"He is more of a modern-day inside forward who likes to receive the ball in the pockets. We both have different attributes but we like playing differently in different styles. He will get the ball on the half-turn and stride through the middle of the pitch. I like to be completely out wide.
"That’s the noticeable difference in the way we play. He is a bit more bulldog-ish than me with his running technique. I like to think I am more elegant and glide across the pitch. We have always played in the same team up until the first-team level. We even played in the same England youth teams.
"We have done the whole journey together. It got to the point where he went to Newcastle and that was hard for me to take. We did everything together. He coped with it better than I did because he had six or seven loans in the meantime.
"He was coming back to Norwich as a base. It was okay because I thought he was always coming back. When he moved to Newcastle, his career went one way and mine went the other way. Hopefully, our paths cross again."
Part of Murphy's ambition is built on his love for the sport, which he still holds close.
Growing up in London, being a fan of Newcastle but being built at Norwich City, Murphy has taken a different path to many around him.
"I am a Newcastle fan, so growing up it would always be Alan Shearer [who I watched]. Then it was [Jermain] Defoe because I was all about scoring goals. So it would be those sorts of players who were hot at the time.
"When I was getting older it would be wingers who I would aspire to be like. Like Bale and Neymar. Like all the top wingers, I just try to be the best I can be. There are loads of things.
"I want to learn and improve. That will come down to me. I want to get more goals so that’s something I will strive on."